Page "Corner reflector" Paragraph 3

The incoming ray is reflected three times, once by each surface, which results in a reversal of direction.

To see this, the three corresponding normal vectors of the corner's perpendicular sides can be considered to form a basis ( a rectangular coordinate system ) ( x, y, z ) in which to represent the direction of an arbitrary incoming ray, b, c. When the ray reflects from the first side, say x, the ray's x component, a, is reversed to-a while the y and z components are unchanged, resulting in a direction of b, c. Similarly, when reflected from side y and finally from side z, the b and c components are reversed.

So the ray direction goes from b, c to b, c to-b, c to-b ,-c and it leaves the corner reflector with all three components of direction exactly reversed.